Transcript DRAFT IS:800 - Structural Engineering Forum of India

PLATE GIRDERS
Built-up sections with deep thin webs
susceptible to buckling in shear
Dr S R Satish Kumar, IIT Madras
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Types of Plate Girders
• Unstiffened Plate Girder
flange plates
web plate
• Transversely Stiffened Plate Girder
ITS
BS
• Transversely and Longitudinally Stiffened Plate Girder
LS
Dr S R Satish Kumar, IIT Madras
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SHEAR RESISTANCE OF
STIFFENED GIRDER
Shear resistance of a web
• Pre-buckling behaviour (Stage 1)
– Requirements of equilibrium in an element inside a
square web plate subject to a shear stress result in
generation of complementary shear stresses
– This results in element being subjected to principal
compression along one diagonal and tension along
the other
Dr S R Satish Kumar, IIT Madras
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Shear resistance of a web - 1
q
B
A
q
q
E
45o
D
q
C
Unbuckled Shear panel
Dr S R Satish Kumar, IIT Madras
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BUCKLING OF WEB PLATES IN SHEAR
cr
Shear buckling of a plate
Dr S R Satish Kumar, IIT Madras
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Shear resistance of a web - 2
– As the applied loading is incrementally enhanced,
plate will buckle along direction of compressive
diagonal - corresponding shear stress in plate
is“critical shear stress”
– Critical shear stress in such a case is given by
 2E
t
qcr  k s
 
12 1   2   d 


– Boundary conditions
supported
Dr S R Satish Kumar, IIT Madras
2
assumed
to
be
simply
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Shear resistance of a web - 3
• shear buckling coefficient (ks) given by
2
c
d 
k s  5.35  4   where  1, i.e. for wide panels
d
c
2
c
d 
k s  5.35    4 where  1, i.e. for webs with closely
d
c
spaced transverse stiffeners
d
Dr S R Satish Kumar, IIT Madras
c
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• Post buckled behaviour (Stage 2)
– Compression diagonal is unable to resist any
more loading beyond elastic critical stress
– Any further increase in shear load is supported
by a tensile membrane field, anchored to top
and bottom flanges and adjacent stiffener
members on either side of web
– Total state of stress in web plate may be
obtained by superimposing post-buckled
membrane tensile stresses upon critical shear
stress
Dr S R Satish Kumar, IIT Madras
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Post buckled behaviour - 1
Anchoring of Tension Field
Dr S R Satish Kumar, IIT Madras
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Tension field action
Dr S R Satish Kumar, IIT Madras
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• Collapse behaviour (Stage 3)
– When load is further increased, tensile
membrane stress continues to exert an
increasing pull on flanges
– Eventually resultant stress obtained by
combining the buckling stress and membrane
stress reaches yield value for web - can be
determined by Von-Mises yield criterion
Dr S R Satish Kumar, IIT Madras
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Collapse behaviour - 1
Tensile membrane stress at yield
Collapse of the panel
Dr S R Satish Kumar, IIT Madras
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Three phases of tension field action
Pre-buckling
Dr S R Satish Kumar, IIT Madras
post-buckling
collapse
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ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS
Transverse stiffeners play important role
by increasing web buckling stress
by supporting tension field after web buckling
by preventing tendency of flanges to get pulled
towards each other
Stiffeners should possess sufficient rigidity
to ensure that they remain straight, while
restricting buckling to individual web panels
Dr S R Satish Kumar, IIT Madras
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ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS - 1
Force imposed on transverse stiffeners by tension field
Dr S R Satish Kumar, IIT Madras
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GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS
 Generally located in compression zones of girder
 Main function - to increase buckling resistance of
web
 When it is subject predominantly to shear would
develop a collapse mechanism, provided
stiffeners remained rigid up to failure
 Once one of sub panels has buckled, post
buckling tension field develops over whole depth
of web panel and influence of stiffeners may be
neglected
Dr S R Satish Kumar, IIT Madras
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GENERAL BEHAVIOUR OF
LONGITUDINALLY STIFFENED GIRDERS – 1
Longitudinal and Transverse stiffeners
Dr S R Satish Kumar, IIT Madras
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8.4 Shear
The factored design shear force, V, in a beam due to
external actions shall satisfy
V  Vd
Vd = design strength calculated as , Vd = Vn / γm0
8.4.1 The nominal plastic shear resistance under pure
shear is given by:
Vn = Vp
Vp 
Av f yw
3
Av = shear area
Cont…
Dr S R Satish Kumar, IIT Madras
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8.4.2 Resistance to Shear Buckling
for an unstiffened web
d
tw
 67
  kv
  250 / f y
for a stiffened web
a) Simple Post-Critical Method
The nominal shear strength is
Vn = Vcr Vcr = d twb
b = shear stress corresponding to buckling,
b) Tension Field Method
The nominal shear strength is
V n = V tf
Dr S R Satish Kumar, IIT Madras
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8.4.2.2 Shear Buckling Design Methods
a) Simple Post-Critical Method -The nominal shear strength is
Vn = Vcr Vcr = d twb
b = shear stress corresponding to buckling, determined as follows:
a) When w < 0.8
 b  f yw / 3
b) When 0.8 < w < 1.25

 b  1  0.625w  0.8 f yw / 3

b
c) When w 1.25
b =0.9 fyw/(3w2)
Cont…
Dr S R Satish Kumar, IIT Madras
0.8
1.25
w
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λw = non -dimensional web slenderness ratio for shear buckling stress,
given by
w 
f yw ( 3  cr ,e )
The elastic critical shear stress of the web, cr is given by:
kv 2 E
 cr 
2
12 1   2 d / t w 


kv = 5.35 when transverse stiffeners are provided only at supports
= 4.0 +5.35 /(c/d)2
for c/d < 1.0
= 5.35+4.0 /(c/d)2
for c/d  1.0
Cont…
Dr S R Satish Kumar, IIT Madras
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b) Tension Field Method - the nominal shear resistance, Vn, should be
Vn=Vtf

Vtf  d tw  b  0.9 wtf tw f v sin 

 Vnp
fv = yield strength of the tension field obtained from

f v  f yw  3  b 
2
2

2 0.5
 =1.5 b sin 2

d
 tan 1  
c
 = inclination of the tension field
2  M fr 
s


The width of the tension field, wtf, is given by:
sin   f y t w 
wtf = d cos – (c-sc-st) sin 

M fr  0.25b f t f f yf 1  N f / b f t f f yf /  m0 
2
Dr S R Satish Kumar, IIT Madras
2

0.5
c
sc
wtf
c
st
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8.6 Design of Beams and Plate Girders with Solid Webs
8.6.1 Minimum Web Thickness
8.6.1.1 Serviceability Requirement
a) when transverse stiffeners are not provided
d
 180  (web connection by flanges along both longitudinal edges)
tw
d
 90 (web connection by flanges along one longitudinal edge only)
tw
b) when transverse stiffeners only are provided;
i)
when c  d
d
 200 w
tw
ii) when 0.74 d < c < d
c
 200 w
tw
iii) when c < 0.74 d
d
 270 w
tw
Dr S R Satish Kumar, IIT Madras
Cont…
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c) when transverse and longitudinal stiffeners are provided
level only
(0.1 d from compression flange)
d
tw
i) when c > d
ii) when 0.74 d < c < d
iii) when c < 0.74 d
at one
 250 w
c
 250 w
tw
d
 340 w
tw
d) when a second longitudinal stiffener (located at neutral axis is
provided )
d
 400 w
tw
Cont…
Dr S R Satish Kumar, IIT Madras
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Design Procedure
Initial Sizing
1)
Taking L/d as 15, calculate min. d and provide suitably
2)
Afreqrd. = BM/ (fy/mo)d ; using bf = 0.3d select flange plate
Also calculate Nf = axial force in the flange
3)
Check that flange criteria gives a plastic section
b = (bf – tw)/2 and b/ tf < 7.9
4)
Web thickness for serviceability 67 < d/ tw < 200
choose such that tw > d/200
5)
Check for flange buckling into web
Assuming c >1.5d , d/ tw < 3452
Dr S R Satish Kumar, IIT Madras
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Design Procedure
6)
Check for shear capacity of web
V < Vd = Vn/ mo; Vn = A (fyw /3) or Vcr
7)
Check for calculating resistance to shear buckling
d/ tw > 67 (kv/5.35) use kv for c/d > 1
8)
Simple post-critical method
Vcr = d tw b where b = (w) and w = (cr )
9)
If V < Vcr/ mo then safe else tension field calculation
reqrd.
10) Vn = Vtf = (fv and ); also calculate Mfv = (Nf )
If V < Vn/ mo safe ! else revise design
Dr S R Satish Kumar, IIT Madras
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Design Procedure
• 8.7 Stiffener design
– a) Intermediate Transverse Web Stiffener  To improve
the buckling strength of slender web due to shear.
– b) Load Carrying Stiffener  To prevent local buckling of
the web due to concentrated loading.
– c) Bearing Stiffener  To prevent local crushing of the
web due to concentrated loading .
– d) Torsion Stiffener  To provide torsional restraint to
beams and girders at supports.
– e) Diagonal Stiffener To provide local reinforcement to
a web under shear and bearing.
–
f) Tension Stiffener  To transmit tensile forces applied
to a web through a flange.
Dr S R Satish Kumar, IIT Madras
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Design Procedure
11)
End panel design – check as a beam between flanges
H q  1.25.Vdp (1  Vcr / Vdp )
Rtf = Hq/2
Rtf
Av = c t and Vtf = Av (fy /3) > Rtf
12)
c
Mtf = Hqd/10
MR = tc3/12*fyd / (c/2) > Mtf
13)
14)
Intermediate Transverse Stiffener Design
i) decide to provide stiffener on one side or both sides
ii) choose tq > tw ; outstand bs < 14tq also < b
check for minimum stiffness
for c = 1.5d, c > 2 d giving
Cl.8.7.2.4 p91
I prov. = (bs-tw/2)3 tq/12 > 0.75dtw3
Dr S R Satish Kumar, IIT Madras
bs
tq
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Design Procedure
15)
Check for Buckling
Cl.8.7.2.5 p91
Stiffener force, Fq = V - Vcr/mo  Fqd
Buckling Resist. Pq with 20tw on either side Cl.8.7.1.5 p90
Calculate Ixx and A, rxx = (Ixx/A)
Leff = 0.7d,  = Leff/rxx, Find fc
Pq = fc A > Fq
bs
16)
tq Cl.8.7.2.6 p92
Connection to web
shear = tw2 / 8bs kN/mm choose appropriate weld size
19)
Check for Intermediate Stiffener under Load
Fq  Fx
Fqd
Dr S R Satish Kumar, IIT Madras

Cl.8.7.2.5 p91
Fx
M
 s 1
Fxd M ys
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